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Math Help - Functional Transformation

  1. #1
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    Functional Transformation

    If  F(x)= sqrt(x) , describe the transformation from  F(x) to  G(x) if  G(x) = -f(-x+1)-7
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    Re: Functional Transformation

    Quote Originally Posted by Gragadoodle View Post
    If  F(x)= sqrt(x) , describe the transformation from  F(x) to  G(x) if  G(x) = -f(-x+1)-7
    is f function the same as F function with different argument? if so, then G(x) = -sqrt(-x + 1) - 7 for x <= 1
    Last edited by votan; October 5th 2013 at 07:18 AM.
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  3. #3
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    Re: Functional Transformation

    If, alternatively, you are looking for a description of the graph of the new function (i.e. shifts/rotations about lines/stretching/skewing/etc.), then break it down step-by-step.

    Compare the graph of f(x) to the graph of f(x-1). Then compare those to the graph of f(-(x-1)) = f(-x+1). Next, compare them to the graph of -f(-x+1). Finally, put it all together as you compare it to the graph of -f(-x+1)-7.
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    Re: Functional Transformation

    Quote Originally Posted by SlipEternal View Post
    If, alternatively, you are looking for a description of the graph of the new function (i.e. shifts/rotations about lines/stretching/skewing/etc.), then break it down step-by-step.

    Compare the graph of f(x) to the graph of f(x-1). Then compare those to the graph of f(-(x-1)) = f(-x+1). Next, compare them to the graph of -f(-x+1). Finally, put it all together as you compare it to the graph of -f(-x+1)-7.
    Yes, I have no idea how to break it down, but this is what I'm looking for.
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    Re: Functional Transformation

    bump
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    Re: Functional Transformation

    Let's consider what happens when we plug in numbers. If we plug in 5 to f(x-1), we get f(5-1) = f(4). Going from the graph of f(x) to the graph of f(x-1), the x-position of f(4) is going from x=4 to x=5. In other words, it is shifting to the right one unit. Now let's consider f(-(x-1)). Now, f(-4) is at x=-4 in our original graph, but it is at x=5 in this graph. Does this mean it is shifting to the right nine units? Not quite. Let's look at some more data to see what's happening. f(-3) is the y-value at x=-3 in our original graph, but it is the y-value at x=4 in f(-(x-1)). So now the shift is only 7 units. The negative sign is actually creating a reflection across some axis. The closer we get to x=1, the less the points need to shift from the original function to our new function. In other words, this is a reflection across the line x=1. Next, -f(-x+1) is taking the value f(-x+1) and taking its reflection across the x-axis. Finally, -f(-x+1)-7 is taking the graph of -f(-x+1) and shifting it down seven units.
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